The resistant virtues of the structure that we make depend on their form; it is through their form that they are stable and not because of an awkward accumulation of materials. There is nothing more noble and elegant from an intellectual viewpoint than this; resistance through form.
Dieste's unique and innovative method of design, a melding of architecture and engineering, elevated these often humble buildings to masterworks of art.
There are deep moral/practical reasons for our search which give form to our work: with the form we create we can adjust to the laws of matter with all reverence, forming a dialogue with reality and its mysteries in essential communion... For architecture to be truly constructed, the materials must be used with profound respect for their essence and possibilities; only thus can 'cosmic economy' be achieved... in agreement with the profound order of the world; only then can have that authority that so astounds us in the great works of the past.
Wang tiles (Hao Wang, 1961) are a class of formal systems. They are modelled visually by square tiles with a color on each side. A set of such tiles is selected, and copies of the tiles are arranged side by side with matching colors, without rotating or reflecting them.
The basic question about a set of Wang tiles is whether it can tile the plane or not, i.e., whether an entire infinite plane can be filled this way. The next question is whether this can be done in a periodic pattern.
In 1966, Wang's student Robert Berger solved the problem in the negative. He proved that no algorithm for the problem can exist, by showing how to translate any Turing machine into a set of Wang tiles that tiles the plane if and only if the Turing machine does not halt. The undecidability of the halting problem then implies the undecidability of Wang's tiling problem.